相关论文: Resolutions by mapping cones
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
Ford circles are parameterized by the rational numbers but are also the result of an iterative geometric procedure. We review this and introduce an apparently new parameterization by solutions of a certain quadratic Diophantine equation. We…
We study rectangles inscribed in lines in the plane by parametrizing these rectangles in two ways, one involving slope and the other aspect ratio. This produces two paths, one that finds rectangles with specified slope and the other…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
By a fixed continuous map from a $3$-space to itself, a knot in the $3$-space may be mapped to another knot in the $3$-space. We analyze possible knot types of them. Then we map a knot repeatedly by a fixed continuous map and analyze…
In this paper we study the existence of solutions of thedegererate elliptic system.
We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…
A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in…
We derive a closed-form expression for the projection onto a capped rotated second-order cone -- a convex set that arises in perspective relaxations of nonlinear programs with binary indicator variables. The closed-form solution involves…
We survey recent results on determinantal processes, random growth, random tilings and their relation to random matrix theory.
In this paper, we consider the convolutions of slanted half-plane mappings and strip mappings and generalize related results in general settings. We also consider a class of harmonic mappings containing slanted half-plane mappings and strip…
In this paper we study minimal free resolutions of some classes of monomial ideals. we first give a sufficient condition to check the minimality of the resolution obtained by the mapping cone. Using it, we obtain the Betti numbers of…
The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the~field of applied geometry. An~isophote on a surface is a curve consisting of surface points whose normals form a constant angle with some…
We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…
Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…
In this paper we use a natural iteration technique to prove existence of solutions to nonlinear Dirichlet problems. Among the examples included is the prescribed mean curvature equation. The nature of the technique allows applications to…
A free resolution of free partially commutative monoids is constructed and with its help the homological dimension of these monoids is calculated.
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
The main purpose of the present paper is to study the numerical properties of supersolvable resolutions of line arrangements. We provide upper-bounds on the so-called extension to supersolvability numbers for certain extreme line…